We consider the convergence of the biorthogcnal series corresponding to the nonselfadjoint Sturm-Liouville operator at the points of discontinuity of its coefficients. For any function $f(x)\in L_2$ we construct a function $\tilde f_{x_0}(x)$ such that the trigonometrical Fourier series of $\tilde f_{x_0}(x)$ is convergent at the point of discontinuity $x_0$ if and only if the biorthogonal series of $f(x)$ is convergent at this point.